A construction of equivariant bundles on the space of symmetric forms

Ada Boralevi (1) , Daniele Faenzi (2) , Paolo Lella (3)

1 Dipartimento di Scienze Matematiche
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 POLIMI - Dipartimento di Matematica [Politecnico Milano]

We construct stable vector bundles on the space P ((SCn+1)-C-d) of symmetric forms of degree d in n + 1 variables which are equivariant for the action of SLn+1 (C) and admit an equivariant free resolution of length 2. For n = 1, we obtain new examples of stable vector bundles of rank d - 1 on P-d, which are moreover equivariant for SL2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.

Mots clés: Stable vector bundles; symmetric forms; group action; equivariant resolution; constant rank matrix; homogeneous bundle; homogeneous variety; quiver representation

Domaines: Mathématiques [math]

Ada Boralevi, Daniele Faenzi, Paolo Lella. A construction of equivariant bundles on the space of symmetric forms. Revista Matemática Iberoamericana, 2022, 38 (3), pp.761-782. ⟨10.4171/RMI/1307⟩. ⟨hal-03927466⟩